Rose-Hulman Institute of Technology
Department of Mechanical Engineering
ME 536
Comput Intell in Control Engr
Project 2:
Course Value: 250 points
Deadline: May 16, 2016
Fuzzy stick balancing.
a) [200 points] Design a fuzzy controller to balance the inverted pendulum. Pay careful
attention to the coordinate definitions shown in the figure below, these are used in the
Simulink model. Ignore the disk position dynamics for this part. Demonstrate that you can
stabilize the virtual dynamics included in the simulink file: Provide plots of all four plant
states, and the control effort.
Figure 1. Schematic of an inverted disk-pendulum system.
b) [25 points] Add disk position control to your stick balancing fuzzy controller. Demonstrate
stability and improved disk position tracking on the simulink model. Provide plots of all four
plant states, and the control effort.
Figure 2: Furuta-Pendulum Simulink Laboratory Configuration
Figure 3. Simulink model (‘Encoder_reset.slx’) for resetting the encoder separately from a closed-loop
trial
c) [25 points] Implement your solution to parts a) and b) on the hardware in C-116. Provide
plots of the hardware response compared to the model response. Position the disk (cart) and
pendulum at zero (vertical hanging position) and run Encoder_reset.slx. In the model
'fuzzyrip.slx' connect to target. Now lift the pendulum to the vertical inverted pendulum.
Have your lab partner start the simulation (play button), and release the pendulum.
HINTS: If you use all four system states as inputs to your fuzzy controller, and allocate five
membership functions to each input state, a 'full' rule set would consist of 54 = 625 rules. This
would be daunting, and frankly overkill. Part a) can be satisfied with 25 rules, considering
only θ and θ& as inputs. If you consider the solution to part b) a 'separate' fuzzy controller, and
try to limit the number of relevant inputs, you should be able to improve cart position tracking
using 25 to 125 additional rules (less would be better from the standpoint of elegance and
computational efficiency). Take advantage of the Fuzzy control property of automatically
balancing conflicting objectives by designing a) and b) separately and implementing them
simultaneously. The master's thesis "Three-Input Fuzzy Controller for a Cart and Inverted
Pendulum System", by Hui Zhao is available at the library. You might find it helpful for parts
a) and b) although the system used was the 'large scale' pendulum, and the sign conventions
are different than those used in our model.
Be sure to iterate your design on Simulink only. I will provide a simulink model of the
linearized pendulum dynamics in inverted mode. A snapshot of the model appears below.
Figure 4: Simulink Model of Furuta Pendulum.